Irreducible Subgroups of GL 1(D) Satisfying Group Identities

R. Ebrahimian, D. Kiani, Mahdavi-Hezavehi
2005 Communications in Algebra  
Let D be a finite dimensional F -central division algebra, and G be an irreducible subgroup of D * := GL 1 (D). Here we investigate the structure of D under various group identities on G. In particular, it is shown that when [D : F ] = p 2 , p a prime, then D is cyclic if and only if D * contains a nonabelian subgroup satisfying a group identity.
doi:10.1081/agb-200058549 fatcat:hv2ryiedgbaqfdjiepyqlhbv7q